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Question
Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is 25.
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Solution
The equation of the line with intercepts a and b is \[\frac{x}{a} + \frac{y}{b} = 1\].
Here, a = b and ab = 25
\[\therefore a \times a = 25\]
\[ \Rightarrow a^2 = 25\]
\[ \Rightarrow a = 5 \left( \because \text { we are to take only positive value of intercepts } \right)\]
Hence, the equation of the required line is
\[\frac{x}{5} + \frac{y}{5} = 1\]
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